1. Field of the Invention
This invention relates to a method of generating globoid worm gears and worm wheels and, more particularly, to an improved method of cutting a globoid worm gear having a conical intervening gear tooth surface.
2. Prior Art
A globoid worm gear pertaining to the invention is based upon the principles disclosed in the treatise entitled "A Study on Hourglass Worm Gearing with Envelopable Tooth Surfaces" whose authors included the inventors of the present invention and which was published in the "Transactions of the American Society of Mechanical Engineers," Volume 100, Journal of Mechanical Design, pages 451-459 (1978).
While the devices taught by the prior art are in actual use, the inclination angle of the intervening gear axes is zero. This corresponds to the application of a conical surface in lieu of a straight line for the gear surface of a revolving worm gear cutting tool for a classical Hindley globoid worm gear.
FIG. 4 illustrates the principles presented in "An Investigation on Secondary Action on Skew Gears" authored by the present inventors, and published in Transactions of the Japan Society of Mechanical Engineers, Vol. 38, No. 311, 1972. In a conventional Hindley globoid worm gear, a satisfactory mesh terminates at a point on a common axis or line which is perpendicular to both gear axes at a limit normal line point and at an edge line B in the central part of a worm wheel A. Based on the principles taught in "An Investigation on Secondary Action on Skew Gears," the edge line B is defined by the appearance of the straight cutting edge in the worm gear cutting tool and defines the first gear surface.
A second gear surface D (commonly called an envelope surface) has a relatively small radius of curvature and effects satisfactory engagement. Second gear surface D appears in the central part of the worm wheel A adjacent the edge line B. On the opposite side of the second gear surface D, there is an imaginary gear surface, which is produced theoretically on the inner side of the worm (i.e., inner side in the thickness direction of the tooth portion). This gear surface is a curved surface and is a trace of the motion of the cutting surface of a tool representing the worm wheel.
The prior art discloses the generation of globoid worm gears by replacing the straight tool used for cutting the classical Hindley globoid worm gears with a tool having a conical cutting surface. As shown in FIG. 5a, the tooth surface G of the worm wheel A is an envelope for second tooth surface D' of conical tool F, both being adjacent to each other within the boundary defined by the central edge line B of the Hindley globoid worm gear.
On the wheel tooth surface shown in FIG. 5b, the mesh is represented by first contact lines 1H.sub.1, 1H.sub.2 . . . , second contact lines 2H.sub.1, 2H.sub.2 . . . , etc. As shown in FIG. 6, the orbital surfaces 1I and 2I intermediate the contact lines intersect along a limit normal point curve J. A pair of contact lines are simultaneously in contact with a surface of a tooth of the worm wheel.
The point P of intersection between the orbital trace surfaces 1I and 2I lies along an axis Z.sub.3 which is perpendicular to the wheel axis Z.sub.1 and worm axis Z.sub.2 and can be taken as a reference of the worm gear design. This means that no real first and second contact lines are obtained in a region close to the worm axis Z.sub.2 beyond point P. Therefore, the limit normal point curve J of the classical Hindley globoid worm gear conicides with a single axis Z.sub.3 perpendicular to the two gear axes. In this case, therefore, satisfactory engagement can be obtained only along one-half of the width of the worm tooth.
A globoid worm gear having a conical intervening gear tooth surface is theoretically the same as the classical Hindley globoid worm gear. On the other hand, discontinuities on the worm wheel tooth surface resulting from the limit normal point curve preclude full engagement in the region beyond the limit normal line point.
A modified method for generating the Hindley globoid worm gear is based on the use of a straight cutting edge and is intended to avoid the inherent problems described above. As shown in FIG. 7, the method performs the gear cutting procedure in three steps by setting different centers 0.sub.1, 0.sub.0 and 0.sub.2 for the revolution of a gear cutting tool K. This method results in trace surfaces for the first and second contact lines which correspond to the individual centers 0.sub.0, 0.sub.1 and 0.sub.2, each having the limit normal point curve spaced from the axis of the worm wheel at each end of the meshed worm gear.
The modified gear generating method which is described hereinabove is based upon the use of a tool employing a straight cutting edge. However, since three different centers of revolution of the tool are used, the number of machining steps is correspondingly increased. The number of machining steps is further increased since it is necessary to separately machine the front tooth and back tooth, i.e., the front tooth surface is generated when it is in contact with the tool and the worm is turned forwards, the back tooth surface being generated when it is in contact with the tool and worm is turned backwards. Further, the setting of the center of revolution of the tool requires considerable time and skill. Further, the individual trace surfaces corresponding to the centers 0.sub.0, 0.sub.1 and 0.sub.2, respectively, of the contact lines are discontinuous between the adjacent machining steps.